In recent years, stream cipher systems have played a big role especially in computer networks. Stream cipher systems depend on pseudo-random (PR) binary key sequences which are mixed with the plaintexts using addition with modulo two to produce the ciphertexts. The PR key sequences are characterized by three properties which defi ne the measure of security for these sequences. These properties are period, complexity and randomness. There are several methods to determine the degree of complexity

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... of these PR sequences like Berlekamp-Massey method, matrices techniques, and using software computing techniques (Neural Networks, Fuzzy Logic and Genetic Algorithms). This paper presents a proposed method to determine the degree of complexity of these PR sequences using one of the properties of the Z-transform which is periodic sequence property. This proposed method enable us to compute the degree of complexity of any periodic sequence produced from linear or nonlinear generators and accurate results are obtained. The steps of the proposed procedure are given, two different examples are illustrated, one of them for a PR sequence over GF(2), and the second example for PR sequence over GF(5).